Performing a musical session via networks requires real-time interaction. There exists, however, the problem of delay between the network nodes, which causes musical sessions become an impediment. To overcome this problem, we have proposed a new protocol for musical session called Mutual Anticipated Session (M.A.S.), which is a type of ensemble that controls appropriate timing of sounds. In the M.A.S, one player's performance precedes the other players', thus this performance is called a "precedent musical performance," and we call a time lapse between the players' performance as "precedent time." In the current M.A.S, it is assumed that the tempo during the performance is constant. In such a case, however, players' requirements to perform more expressively or more emotionally by varying the tempo are sacrificed. Thus, in this paper, enhancement of function that accommodates changes of the tempo by predicting tendency of it is realized. Finally we evaluate the enhancement both by system performance test and by task performance of subject experiments.